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Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics. It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry.
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The Geometry of Exponential Families. Calculus on Manifolds. Statistical Manifolds. Connections. Curvature. Information Metrices and Statistical Divergences. Asymptotics. Bundles and Tensors. Higher Order Geometry. References. Index.Product Description:
Book by Murray MK Rice JW
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Descrizione libro 1993. HRD. Condizione: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice articolo VT-9780412398605
Descrizione libro Chapman and Hall/CRC. Condizione: New. Hardcover. Worldwide shipping. FREE fast shipping inside USA (express 2-3 day delivery also available). Tracking service included. Ships from United States of America. Codice articolo 0412398605
Descrizione libro Chapman and Hall/CRC, 1993. HRD. Condizione: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice articolo F9-9780412398605
Descrizione libro Taylor Francis Ltd, United States, 2014. Hardback. Condizione: New. Softcover Reprint of the Origi ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its higher-order aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families. Codice articolo BTE9780412398605
Descrizione libro Chapman and Hall/CRC, 2018. Hardback. Condizione: NEW. 9780412398605 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Print on Demand title, produced to the highest standard, and there would be a delay in dispatch of around 10 working days. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Codice articolo HTANDREE0246886
Descrizione libro Chapman & Hall, 1993. Hardcover. Condizione: Brand New. 1st edition. 288 pages. 9.00x5.50x0.75 inches. In Stock. Codice articolo __0412398605
Descrizione libro Chapman and Hall/CRC, 1993. Hardcover. Condizione: New. Never used!. Codice articolo P110412398605
Descrizione libro 1993. Hardcover. Condizione: New. 1st. Hardcover. Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions there has been interest among statisticians in the applica.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 292 pages. 0.540. Codice articolo 9780412398605